# Numerical Integration in Python

Learn how to integrate a sequence or list of values numerically

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In [1]:

```
import plotly.plotly as py
import plotly.graph_objs as go
from plotly.tools import FigureFactory as FF
import numpy as np
import pandas as pd
import scipy
```

#### Integrate the Sine Function¶

How to use numerical integration to find the area of $y = sin(x)$ between $0$ and $2\pi$.

In [2]:

```
x = np.linspace(0, 2*np.pi, 100)
y = np.sin(x)
trace1 = go.Scatter(
x=x,
y=y,
mode='lines',
)
# use numpy's built in trapezoid-rule integration tool
dy = np.trapz(y, x)
annotation = go.Annotation(
x=4.5,
y=1.25,
text='Numerical Integration of sin(x) is approximately %s' % (dy),
showarrow=False
)
layout = go.Layout(
annotations=[annotation]
)
trace_data = [trace1]
fig = go.Figure(data=trace_data, layout=layout)
py.iplot(fig, filename='1d-numerical-integration')
```

Out[2]: